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69
Being Bayesian about network structure
 Machine Learning
, 2000
"... Abstract. In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model sel ..."
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Cited by 270 (4 self)
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Abstract. In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have nonnegligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior “landscape”. We present empirical results on synthetic and reallife datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a nonBayesian bootstrap approach.
Exact Bayesian structure discovery in Bayesian networks
 J. of Machine Learning Research
, 2004
"... We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n2 n) time, where n is the number of attributes; the number of parents per ..."
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Cited by 102 (12 self)
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We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n2 n) time, where n is the number of attributes; the number of parents per attribute is bounded by a constant. In this paper we show that the posterior probabilities for all the n(n−1) potential edges can be computed in O(n2 n) total time. This result is achieved by a forward–backward technique and fast Möbius transform algorithms, which are of independent interest. The resulting speedup by a factor of about n 2 allows us to experimentally study the statistical power of learning moderatesize networks. We report results from a simulation study that covers data sets with 20 to 10,000 records over 5 to 25 discrete attributes. 1
Learning Bayesian Networks by Genetic Algorithms. A case study in the prediction of survival in malignant skin melanoma
, 1997
"... In this work we introduce a methodology based on Genetic Algorithms for the automatic induction of Bayesian Networks from a file containing cases and variables related to the problem. The methodology is applied to the problem of predicting survival of people after one, three and five years of being ..."
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Cited by 98 (11 self)
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In this work we introduce a methodology based on Genetic Algorithms for the automatic induction of Bayesian Networks from a file containing cases and variables related to the problem. The methodology is applied to the problem of predicting survival of people after one, three and five years of being diagnosed as having malignant skin melanoma. The accuracy of the obtained model, measured in terms of the percentage of wellclassified subjects, is compared to that obtained by the called NaiveBayes. In both cases, the estimation of the model accuracy is obtained from the 10fold crossvalidation method. 1. Introduction Expert systems, one of the most developed areas in the field of Artificial Intelligence, are computer programs designed to help or replace humans beings in tasks in which the human experience and human knowledge are scarce and unreliable. Although, there are domains in which the tasks can be specifed by logic rules, other domains are characterized by an uncertainty inherent...
An Indexed Bibliography of Genetic Algorithms in Power Engineering
, 1995
"... s: Jan. 1992  Dec. 1994 ffl CTI: Current Technology Index Jan./Feb. 1993  Jan./Feb. 1994 ffl DAI: Dissertation Abstracts International: Vol. 53 No. 1  Vol. 55 No. 4 (1994) ffl EEA: Electrical & Electronics Abstracts: Jan. 1991  Dec. 1994 ffl P: Index to Scientific & Technical Proceed ..."
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Cited by 87 (10 self)
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s: Jan. 1992  Dec. 1994 ffl CTI: Current Technology Index Jan./Feb. 1993  Jan./Feb. 1994 ffl DAI: Dissertation Abstracts International: Vol. 53 No. 1  Vol. 55 No. 4 (1994) ffl EEA: Electrical & Electronics Abstracts: Jan. 1991  Dec. 1994 ffl P: Index to Scientific & Technical Proceedings: Jan. 1986  Feb. 1995 (except Nov. 1994) ffl EI A: The Engineering Index Annual: 1987  1992 ffl EI M: The Engineering Index Monthly: Jan. 1993  Dec. 1994 The following GA researchers have already kindly supplied their complete autobibliographies and/or proofread references to their papers: Dan Adler, Patrick Argos, Jarmo T. Alander, James E. Baker, Wolfgang Banzhaf, Ralf Bruns, I. L. Bukatova, Thomas Back, Yuval Davidor, Dipankar Dasgupta, Marco Dorigo, Bogdan Filipic, Terence C. Fogarty, David B. Fogel, Toshio Fukuda, Hugo de Garis, Robert C. Glen, David E. Goldberg, Martina GorgesSchleuter, Jeffrey Horn, Aristides T. Hatjimihail, Mark J. Jakiela, Richard S. Judson, Akihiko Konaga...
Orderingbased search: A simple and effective algorithm for learning Bayesian networks
 In UAI
, 2005
"... One of the basic tasks for Bayesian networks (BNs) is that of learning a network structure from data. The BNlearning problem is NPhard, so the standard solution is heuristic search. Many approaches have been proposed for this task, but only a very small number outperform the baseline of greedy hill ..."
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Cited by 74 (0 self)
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One of the basic tasks for Bayesian networks (BNs) is that of learning a network structure from data. The BNlearning problem is NPhard, so the standard solution is heuristic search. Many approaches have been proposed for this task, but only a very small number outperform the baseline of greedy hillclimbing with tabu lists; moreover, many of the proposed algorithms are quite complex and hard to implement. In this paper, we propose a very simple and easytoimplement method for addressing this task. Our approach is based on the wellknown fact that the best network (of bounded indegree) consistent with a given node ordering can be found very efficiently. We therefore propose a search not over the space of structures, but over the space of orderings, selecting for each ordering the best network consistent with it. This search space is much smaller, makes more global search steps, has a lower branching factor, and avoids costly acyclicity checks. We present results for this algorithm on both synthetic and real data sets, evaluating both the score of the network found and in the running time. We show that orderingbased search outperforms the standard baseline, and is competitive with recent algorithms that are much harder to implement. 1
Feature Subset Selection by Bayesian networks: a comparison with genetic and sequential algorithms
"... In this paper we perform a comparison among FSSEBNA, a randomized, populationbased and evolutionary algorithm, and two genetic and other two sequential search approaches in the well known Feature Subset Selection (FSS) problem. In FSSEBNA, the FSS problem, stated as a search problem, uses the E ..."
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Cited by 53 (15 self)
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In this paper we perform a comparison among FSSEBNA, a randomized, populationbased and evolutionary algorithm, and two genetic and other two sequential search approaches in the well known Feature Subset Selection (FSS) problem. In FSSEBNA, the FSS problem, stated as a search problem, uses the EBNA (Estimation of Bayesian Network Algorithm) search engine, an algorithm within the EDA (Estimation of Distribution Algorithm) approach. The EDA paradigm is born from the roots of the GA community in order to explicitly discover the relationships among the features of the problem and not disrupt them by genetic recombination operators. The EDA paradigm avoids the use of recombination operators and it guarantees the evolution of the population of solutions and the discovery of these relationships by the factorization of the probability distribution of best individuals in each generation of the search. In EBNA, this factorization is carried out by a Bayesian network induced by a chea...
Improved learning of Bayesian networks
 Proc. of the Conf. on Uncertainty in Artificial Intelligence
, 2001
"... Two or more Bayesian network structures are Markov equivalent when the corresponding acyclic digraphs encode the same set of conditional independencies. Therefore, the search space of Bayesian network structures may be organized in equivalence classes, where each of them represents a different set o ..."
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Cited by 39 (6 self)
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Two or more Bayesian network structures are Markov equivalent when the corresponding acyclic digraphs encode the same set of conditional independencies. Therefore, the search space of Bayesian network structures may be organized in equivalence classes, where each of them represents a different set of conditional independencies. The collection of sets of conditional independencies obeys a partial order, the socalled “inclusion order.” This paper discusses in depth the role that the inclusion order plays in learning the structure of Bayesian networks. In particular, this role involves the way a learning algorithm traverses the search space. We introduce a condition for traversal operators, the inclusion boundary condition, which, when it is satisfied, guarantees that the search strategy can avoid local maxima. This is proved under the assumptions that the data is sampled from a probability distribution which is faithful to an acyclic digraph, and the length of the sample is unbounded. The previous discussion leads to the design of a new traversal operator and two new learning algorithms in the context of heuristic search and the Markov Chain Monte Carlo method. We carry out a set of experiments with synthetic and realworld data that show empirically the benefit of striving for the inclusion order when learning Bayesian networks from data.
A new approach for learning belief networks using independence criteria
 International Journal of Approximate Reasoning
, 2000
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A Scoring Function for Learning Bayesian Networks based on Mutual Information and Conditional Independence Tests
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2006
"... We propose a new scoring function for learning Bayesian networks from data using score search algorithms. This is based on the concept of mutual information and exploits some wellknown properties of this measure in a novel way. Essentially, a statistical independence test based on the chisquare di ..."
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Cited by 30 (0 self)
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We propose a new scoring function for learning Bayesian networks from data using score search algorithms. This is based on the concept of mutual information and exploits some wellknown properties of this measure in a novel way. Essentially, a statistical independence test based on the chisquare distribution, associated with the mutual information measure, together with a property of additive decomposition of this measure, are combined in order to measure the degree of interaction between each variable and its parent variables in the network. The result is a nonBayesian scoring function called MIT (mutual information tests) which belongs to the family of scores based on information theory. The MIT score also represents a penalization of the KullbackLeibler divergence between the joint probability distributions associated with a candidate network and with the available data set. Detailed results of a complete experimental evaluation of the proposed scoring function and its comparison with the wellknown K2, BDeu and BIC/MDL scores are also presented.
Decomposing Bayesian Networks: Triangulation of Moral Graph with Genetic Algorithms
 Statistics and Computing
, 1997
"... In this paper we consider the optimal decomposition of Bayesian networks. More concretely, we examine  empirically , the applicability of genetic algorithms to the problem of the triangulation of moral graphs. This problem constitutes the only difficult step in the evidence propagation algorithm ..."
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Cited by 26 (4 self)
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In this paper we consider the optimal decomposition of Bayesian networks. More concretely, we examine  empirically , the applicability of genetic algorithms to the problem of the triangulation of moral graphs. This problem constitutes the only difficult step in the evidence propagation algorithm of Lauritzen and Spiegelhalter (1988) and is known to be NPhard (Wen, 1991). We carry out experiments with distinct crossover and mutation operators and with different population sizes, mutation rates and selection biasses. The results are analyzed statistically. They turn out to improve the results obtained with most other known triangulation methods (Kjaerulff, 1990) and are comparable to the ones obtained with simulated annealing (Kjaerulff, 1990; Kjaerulff, 1992). Keywords: Bayesian networks, genetic algorithms, optimal decomposition, graph triangulation, moral graph, NPhard problems, statistical analysis. 1 Introduction The Bayesian networks constitute a reasoning method based on p...